If the equations x2+2x+3=0 and ax2+bx+c=0, a, b, c ∈ R have a common root, then a: b: c is

Question

If the equations x2+2x+3=0 and ax2+bx+c=0, a, b, c ∈ R have a common root, then a: b: c is (A) 1: 2: 3 (B) 3: 2: 1 (C) 1: 3: 2 (D) 3: 1: 2

Tardigrade Admin · Accepted Answer

Given equations are x2+2x+3=0 ...(i) and ax2+bx+c=0 ...(ii) Since, Eq. (i) has imaginary roots, so Eq. (ii) will also have both roots same as Eq. (i). Thus, (a/1)=(b/2)=(c/3) Hence, a: b: c is 1: 2: 3.

Q. If the equations $x^{2} + 2 x + 3 = 0$ and $a x^{2} + b x + c = 0, a, b, c \in R$ have a common root, then $a : b : c$ is

1 : 2 : 3

3 : 2 : 1

1 : 3 : 2

3 : 1 : 2

Given equations are $x^{2} + 2 x + 3 = 0... (i)$
and $a x^{2} + b x + c = 0... (ii)$
Since, Eq. (i) has imaginary roots, so Eq. (ii) will also
have both roots same as Eq. (i).
Thus, $\frac{a}{1} = \frac{b}{2} = \frac{c}{3}$
Hence, $a : b : c$ is $1 : 2 : 3$ .

Q. If the equations x2+2x+3=0 and ax2+bx+c=0,a,b,c∈R have a common root, then a:b:c is